Tuning the Horn - 7th Harmonic

In the series "Tuning the Horn - Engaging with the natural notes of the (French) horn."
Exploring the (French) horn's microtonal possibilities.
Here's a transcript of the video text:
'Welcome to Michael’s Microtonal Method Episode Three.
Let’s delve into the 7th harmonic by starting in the middle of the double horn with Horn in F, no valves.’
Demo
Horn in F Harmonics 1, 2, 3, 4, 5, 6, 7
‘There it is, the 7th harmonic, a narrow minor 7th above the 4th harmonic:’
Harmonic 4 then 7, 7:4
‘Ratio 7,4’
‘A diminished 5th above the 5th harmonic:’
Harmonic 5 then 7, 7:5
‘Ratio 7,5’
‘A narrow minor 3rd above 6th harmonic:’
Harmonic 6 then 7, 7:6
‘Ratio 7,6’
‘A wide major 2nd below the 8th harmonic:’
Harmonic 7 then 8, 8:7
‘Ratio 8,7’
‘A wide major 3rd below the 9th harmonic:’
Harmonic 7 then 9, 9:7
‘Ratio 9,7’
‘An augmented 4th below the 10th harmonic:’
Harmonic 7 then 10, 10:7
‘Ratio 10, 7’
‘I’ll stop there because harmonic 11 brings in the next prime numbered harmonic, the next just intonation limit, the next unique ‘flavour.’ 11 is the topic of the next Episode.’
‘The 7th harmonic gives us a whole bunch of intervals associated with it. For the moment I’ll stay with the F horn and explore the difference between the written B♭, the B♭ from the 3-limit system and from the 5-limit system.’
Demo
F horn C/B♭ horn C B♭ horn F/E♭ horn F E♭ horn B♭ = F horn 1st valve
C F B♭
F horn C F horn (F:0)/B♭ horn G (tune 1st valve high) B♭ horn B♭
C G B♭
F horn C (8th harmonic) F horn B♭ 7th harmonic
’3 B-flats: intonation from the 3-limit, 5-limit, 7-limit systems.’
F horn 1st valve B♭ horn 1st valve F horn no valves
’Here in pitch order descending: 3 B-flats: intonation from the 3-limit, 5-limit, 7-limit systems.’
B♭ horn 1st valve F horn 1st valve F horn no valves
’3 pitches: easy to achieve microtones. Similar microtones can be achieved anywhere on the horn where there is a 7th harmonic. The most interesting examples are at the intersection between a 5th, 6th and 7th harmonic. The note G will do nicely:
Demo
E♭ horn 6th harmonic (F:1) G♭ horn 5th harmonic (B♭ :2,3) C horn 7th harmonic (F:1,3)
E horn 6th harmonic (F:2) G horn 5th harmonic (B♭ :1,2) D♭ horn 7th harmonic (F:2,3)
F horn 6th harmonic (F:0) A♭ horn 5th harmonic (B♭ :1) D horn 7th harmonic (F:1,2)
F♯ horn 6th harmonic (B♭:2,3) A horn 5th harmonic (B♭ :2) E♭ horn 7th harmonic (F :1)
G horn 6th harmonic (B♭:1,2) B♭ horn 5th harmonic (B♭ :0) E horn 7th harmonic (F:2)
A♭ horn 6th harmonic (B♭ :1) B horn 10th harmonic (F :1,2,3) F horn 7th harmonic (F:0)
‘not ideal: hard to tune and hard to focus’
A horn 6th harmonic (B♭ :2) C horn 10th harmonic (F :1,3) F♯ horn 7th harmonic (B♭:2,3)
B♭ horn 6th harmonic (B♭ :0) D♭ horn 10th harmonic (F :2,3) G horn 7th harmonic (B♭ :1,2)
E horn 9th harmonic (F:2) D horn 10th harmonic (F:1,2) A♭ horn 7th harmonic (B♭ :1)
F horn 9th harmonic (F:0) E♭ horn 10th harmonic (F:1) A horn 7th harmonic (B♭ :2)
F♯ horn 9th harmonic (B♭ :2,3) E horn 10th harmonic (F:2) B♭ horn 7th harmonic (B♭ :0)
‘Another beaut thing we can do is to tune a valve slide to match the 7th harmonic of another tube length.’
Demo
F horn 7th harmonic (F:0) tune E♭ horn 8th harmonic (F:1) to the same pitch.
Play E♭ horn 8th harmonic then 7th harmonic.
Play F horn 8th then 7th harmonic,
then E♭ horn 8th harmonic then 7th harmonic
then F horn 6th harmonic (G)
then A♭ then G (ratio 49:48) an interval of 37 cents.
‘I hope you get a feel for the possibilities of using the 7th harmonic.’